We saw in Example 4.4 on page 145 how a Carnot cycle could be set up using steam as a working fluid. The addition of heat at constant temperature and the macroscopic definition of entropy establish a correspondence between temperature and heat addition/removal. Steam is especially well suited for isothermal heat exchange because boiling and condensation are naturally isothermal and exchange large amounts of heat. To review, we could plot this cycle in T-S coordinates and envision a flow process with a turbine to produce work during adiabatic expansion and some type of compressor for the adiabatic compression as shown in Fig. 5.1. The area inside the P-V cycle represents the work done by the gas in one cycle, and the area enclosed by the T-S path is equal to the net intake of energy as heat by the gas in one cycle.
Figure 5.1. Illustration of a Carnot cycle based on steam in T-S coordinates.
The Carnot cycle has a major advantage over other cycles. It operates at the highest temperature available for as long as possible, reducing irreversibilities at the boundary because the system approaches the reservoir temperature during the entire heat transfer. In contrast, other cycles may only approach the hot reservoir temperature for a short segment of the heat transfer. A similar argument holds regarding the low temperature reservoir. Unfortunately, it turns out that it is impossible to make full use of the advantages of the Carnot cycle in practical applications. When steam is used as the working fluid, the Carnot cycle is impractical for three reasons: 1) It is impractical to stay inside the phase envelope because higher temperatures correlate with higher pressure. Higher pressures lead to smaller heat of vaporization to absorb heat. Since the critical point of water is only ~374°C, substantially below the temperatures from combustion, the temperature gradient between a fired heater and the steam would be large; 2) expanding saturated vapor to low-quality (very wet) steam damages turbine blades by rapid erosion due to water droplets; 3) compressing a partially condensed fluid is much more complex than compressing an entirely condensed liquid. Therefore, most power plants are based on modifications of the Rankine cycle, discussed below. Nevertheless, the Carnot cycle is so simple that it provides a useful estimate for checking results from calculations regarding other cycles.
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